Question

Let u= { 1, 2, 3,4,5,6,7} , A = {1,4,6,7}
B = {1,2,3} Find A, B', A intersection B, A Union B and
hence show that (A Union B) = A intersection B​

Answer 1

Answer:

i) A = {1,4,6,7}

ii) B' = {4,5,6,7}

iii) (A n B) = { 1 }

iv) (A u B) = {1,2,3,4,6,7}

Step-by-step explanation:

ii) B' = U - B

B' = { 1,2,3,4,5,6,7} - {1,2,3}

   = {4,5,6,7}

iii) A n B = {1,4,6,7} n {1,2,3}

              = { 1 }

iv) A u B = {1,4,6,7} u {1,2,3}

              ={1,2,3,4,6,7}

To show : A u B = A n B

LHS

A u B = {1,2,3,4,6,7}  → (1)

RHS

A n B = { 1 } → (2)

From (1) and (2) we know that,

LHS ≠ RHS

Hence A u B ≠ A n B